A thorough study of interrelationship in fuzzy implication axioms

Yun Shi; Bart Van Gasse; Da Ruan; Etienne Kerre; Özgür Kabak

doi:10.1142/9789814295062_0008

A thorough study of interrelationship in fuzzy implication axioms

Yun Shi, Bart Van Gasse, Da Ruan, Etienne Kerre, Özgür Kabak

Research output › peer-review

Abstract

A fuzzy implication is an extension of the classical binary implication in fuzzy logic that plays an important role in the approximate reasoning process and in decision making applications. It should satisfy different potential axioms, among which eight axioms are most important. Different authors have investigated the dependence and independence of the eight axioms but the investigation is yet not complete. We study a complete interrelationship of all the eight axioms, and give for each independence case a counter-example.

Original language	English
Title of host publication	Intelligent Decision Making Systems
Place of Publication	Singapore, Singapore
Pages	52-57
Volume	1
DOIs	https://doi.org/10.1142/9789814295062_0008
State	Published - Nov 2009
Event	The 4th Int. ISKE Conference on Intelligent Decision Making Systems - Hasselt Duration: 27 Nov 2009 → 28 Nov 2009

Publication series

Name	Computer Engineering and Information Science
Number	2

Conference

Conference	The 4th Int. ISKE Conference on Intelligent Decision Making Systems
Country/Territory	Belgium
City	Hasselt
Period	2009-11-27 → 2009-11-28

Access to Document

10.1142/9789814295062_0008License: Unspecified

Cite this

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title = "A thorough study of interrelationship in fuzzy implication axioms",

abstract = "A fuzzy implication is an extension of the classical binary implication in fuzzy logic that plays an important role in the approximate reasoning process and in decision making applications. It should satisfy different potential axioms, among which eight axioms are most important. Different authors have investigated the dependence and independence of the eight axioms but the investigation is yet not complete. We study a complete interrelationship of all the eight axioms, and give for each independence case a counter-example.",

keywords = "Fuzzy implications, Fuzzy implication axioms, Approximate reasoning",

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Shi, Y, Van Gasse, B, Ruan, D, Kerre, E & Kabak, Ö 2009, A thorough study of interrelationship in fuzzy implication axioms. in Intelligent Decision Making Systems. vol. 1, Computer Engineering and Information Science, no. 2, Singapore, Singapore, pp. 52-57, The 4th Int. ISKE Conference on Intelligent Decision Making Systems, Hasselt, Belgium, 2009-11-27. https://doi.org/10.1142/9789814295062_0008

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